Standard form
Standard Form
Standard form is used so we can work easily with very long
numbers (large or small)
e.g. 2500000000000000 or 0.000000000006
We do this by multiplying by powers of 10
A number written in standard form will look like this:
a x 10b where a is between 1 and 10 and b is an integer
Powers of 10:
103 = 1000
102 = 100
101 = 10
100 = 1
10-1 =
-2
10 =
𝟏
𝟏𝟎
𝟏
𝟏𝟎𝟎
2500000000000000 = 2.5 x 1015
15
0.000000000006 = 6 x 10-12
12
30000 = 3 x 104
2540000 = 2.54 x106
(÷ 10)
(÷ 100)
0.0547 = 5.47 x 10-2
0.00063 = 6.3 x10-4
Non-calculator standard form
5
7
12
4 x 10 x 2 x 10 = 8 x 10 (4 x 2 = 8) (5 + 7 = 12)
3.2 x 108 x 2 x 10-5 = 6.4 x 103 (3.2 x 2 = 6.4) (8 + -5 = 3)
2 x 106 x 7.8 x 104 = 15.6 x 1010 = 1.56 x 1011
9 x 108 ÷ 2 x 104 = 4.5 x 104 (9 ÷ 2 = 4.5) (8 - 4 = 4)
3 x 1015 ÷ 4 x 102 = 0.75 x 1013 = 7.5 x 1012
5.3 x 109 + 2.1 x 109 = 7.4 x 109
4.8 x 1011 - 1.34 x 1011 = 3.46 x 1011
7.1 x 1025 + 9.73 x 1025 = 16.83 x 1025 = 1.683 x 1026
Add the indices when
multiplying
Your answer must be
in correct standard
form
Subtract the indices
when dividing
Make the indices
the same before
adding or
subtracting
7.2 x 1015 + 3.6 x 1014 = 7.2 x 1015 + 0.36 x 1015 = 7.56 x 1015
8.45 x 1024 - 2.9 x 1023 = 8.45 x 1024 - 0.29 x 1024 = 8.16 x 1024
Learn how to use your calculator to perform harder
standard form questions
© www.teachitmaths.co.uk 2017
27916
Writing out a sum
may help!
Page 1 of 1